Global Conservative Solutions to a Nonlinear Variational Wave Equation

Details Global Conservative Solutions to a Nonlinear Variational Wave Equation Global Conservative Solutions to a Nonlinear Variational Wave Equation

2005-02-02

arxiv.org/abs/math/0502058v1

Mathematics

Analysis of PDEs

32 pages, 6 figures

Scientific paper

10.1007/s00220-006-0047-8

We establish the existence of a conservative weak solution to the Cauchy
problem for the nonlinear variational wave equation $u_{tt} -
c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\cdot)$ is any
smooth function with uniformly positive bounded values.

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